A porosity result in convex minimization

We study the minimization problem f (x) → min, x ∈ C ,w heref belongs to a complete metric space of convex functions and the set C is a countable intersection of a de- creasing sequence of closed convex sets Ci in a reflexive Banach space. Let be the set of all f ∈ for which the solutions of the minimization problem over the set Ci con- verge strongly as i →∞ to the solution over the set C. In our recent work we show that the set contains an everywhere dense Gδ subset of . In this paper, we show that the complement \ is not only of the first Baire category but also a σ-porous set.